The lattice Boltzmann equation for modelling arterial flows: Review and application

Internal Medicine Clinical and Laboratory

Volumn 11, Issue 1-3, 2003, Pages 24-29

  Buick, J M ^d,e   Cosgrove, J A ^d   Tonge, S J ^d   Mulholland, A J ^a   Steves, B A ^b   Collins, M W ^c  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b GLASGOW CALEDONIAN UNIVERSITY   (United Kingdom)

^c LONDON SOUTH BANK UNIVERSITY   (United Kingdom)

^d UNIVERSITY OF EDINBURGH   (United Kingdom)

^e UNIVERSITY OF NEW ENGLAND   (Australia)

Author keywords

Arterial flows; Lattice Boltzmann; Simulation

Indexed keywords

ARTERY BLOOD FLOW; COMPUTER SIMULATION; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; OSCILLATION; REVIEW; SUSPENDED PARTICULATE MATTER;

EID: 2442670258     PISSN: 15909271     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (55)

1. Bonn D. Plaque detection: The key to tackling atherosclerosis? Lancet 1999;354:656.
2. Fry DL. Haemodynamic forces in atherogenesis. In: Cerebrovascular disease. New York: Raven Press 1976:77-95.
3. Caro CG, Fitz-Gerald JM, Schroter RC. Atheroma and arterial wall shear. Observations, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis. Proc R Soc Lond 1971;B171:109-59.
4. Ferréol B, Rothman DH. Lattice-Boltzmann simulations of flow-through Fontainebleau sandstone. Transport Porous Med 1995;20:3-20.
5. Michael A, Spaid A, Phelan Jr. FR. Lattice Boltzmann methods for modeling microscale flow in fibrous porous media. Phys Fluids 1997;9:2468-74.
6. Manwart C, Aaltosalmi U, Koponen A, Hilfer R, Timonen J. Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media. Phys Rev E 2002;66: Article no. 016702.
7. Shan X, Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 1993;47:1815-9.
8. Swift MR, Orlandini E, Osborn WR, Yeomans JM. Lattice Boltzmann simulation of liquid-gas and binary fluid systems. Phys Rev E 1996;54:5041-52.
9. Ladd AJC. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J Fluid Mech 1994;271:285-309.
10. Masselot A, Chopard B. A lattice Boltzmann model for particle transport and deposition. Europhys Lett 1998;42:259-64.
11. Ciofalo M, Collins MW, Hennessy TR. Nanoscale fluid dynamics in physiological processes. A review study. Southampton, Boston: WIT Press 1999.
12. Lim CY, Shu C, Niu XD, Chew YT. Application of lattice Boltzmann method to simulate microchannel flows. Phys Fluids 2002;14:2299-308.
13. Frisch U, Hasslacher B, Pomeau Y. Lattice-gas automata for the Navier-Stokes equation. Phys Rev Lett 1986;56:1505-8.
14. Frisch U, d'Humières D, Hasslacher B, Lallemand P, Pomeau Y, Rivet J-P. Lattice gas hydrodynamics in two and three dimensions. Complex Syst 1987;1:649-707.
15. d'Humières D, Lallemand P. Flow of a lattice gas between two parallel plates and development of the Poiseuille profile. Paris: Computes Rendus de L'Académie des Sciences 1986;302:309-19.
16. d'Humières D, Pomeau Y, Lallemand P. Simulation of 2-D Von Karman streets using a lattice gas. Paris: Computes Rendus de L'Académie des Sciences 1985;301:423-35.
17. d'Humières D, Lallemand P. Lattice gas automata for fluid mechanics. Physica A 1986;140:326-35.
18. d'Humières D, Lallemand P, Searby G. Numerical experiments on lattice gases: Mixtures and Galilean invariance. Complex Syst 1987;1:633-47.
19. Boon JP, Noullez A. Lattice gas hydrodynamics. In: Special course on modern theoretical and experimental approaches to turbulent flow structure and its modelling. AGARD (Advisory Group for Aerospace Research and Development) NATO 1987.
20. Wylie B. Application of two-dimensional cellular automaton lattice-gas models to the simulation of hydrodynamics. PhD thesis, The University of Edinburgh 1990.
21. Wallace D. Scientific computation on SIMD and MIMD machines. Phil Trans R Soc Lond A 1988;326:481-98.
22. Clavin P, Lallemand P, Pomeau Y, Searby G. Simulation of free boundaries in flow systems by lattice-gas models. J Fluid Mech; 188:437-64.
23. McNamara GR, Zanetti G. Use of the Boltzmann equation to simulate lattice-gas automata. Phys Rev Lett 1988;61:2332-5.
24. Chen S, Chen H, Martinez D, Matthaeus W. Lattice Boltzmann model for simulation of magnetohydrodynamics. Phys Rev Lett 1991;67:3776-9.
25. Bhatnagar PL, Gross EP, Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys Rev 1954;94:511-25.
26. Qian YH, d'Humières D, Lallemand P. Lattice BGK models for Navier-Stokes equation. Europhys Lett 1992;17:479-84.
27. Chen S, Doolen GD. Lattice Boltzmann method for fluid flows. Ann Rev Fluid Mech 1998;30:329-64.
28. Cornubert R, d'Humières D, Levermore D. A Knudsen layer theory for lattice gases. Physica D 1991;47:241-59.
29. Noble DR, Georgiadis JG, Buckius RO. Direct assessment of lattice Boltzmann hydrodynamics and boundary conditions for recirculating flows. J Stat Phys 1995;81:17-33.
30. Skordos PA. Initial and boundary conditions for the lattice Boltzmann method. Phys Rev E 1993;48:4823-42.
31. Ziegler DP. Boundary conditions for lattice Boltzmann simulations. J Stat Phys 1993;71:1171-7.
32. Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press 2001.
33. Buick JM, Greated CA. Lattice Boltzmann modeling of interfacial waves. Phys Fluids 1998;10:1490-511.
34. Buick JM, Greated CA, Campbell DM. Lattice BGK simulation of sound waves. Europhys Lett 1998;43:235-40.
35. Benzi R, Succi S. Two-dimensional turbulence with the lattice Boltzmann equation. J Phys A 1990;23:L1-5.
36. Krafczyk M, Cerrolaza M, Schulz M, Rank E. Analysis of 3D transient blood flow passing through an artificial aortic valve by lattice-Boltzmann methods. J Biomech 1998;31:453-62.
37. Krafczyk M, Tölke J, Rank E, Schulz M. Two-dimensional simulation of fluid-structure interaction using lattice-Boltzmann methods. Comput Struct 2001;79:2031-7.
38. Lee CS Chandran KB. Numerical-simulation of instantaneous backflow through central clearance of bileaflet mechanical heart-valves at closure - shear-stress and pressure fields within clearance. Med Biol Eng Comput 1995;33:257-63.
39. Belleman RG, Sloot PMA. Simulated vascular reconstruction in a virtual operating theatre. In: Lemke HU, Vannier MW, Inamura K, Farman, AG, Doi K, eds. CARS 2001: Computer Assisted Radiology and Surgery. Elsevier Science 2001:938-44.
40. Kandhai D, Dubbeldam D, Hoekstra AG, and Sloot PMA. Parallel lattice-Boltzmann simulation of fluid flow in centrifugal elutriation chambers. In: Sloot P, Bubak M, Hertzberger B, eds. High-Performance Computing and Networking - Lecture notes in Computer Science. Springer 1998:173-82.
41. Lin Z, Fang H, Wang Z. Lattice Boltzmann simulation of viscous fluid systems with elastic boundaries. Phys Rev E 1998;57:R25-8.
42. Fang H, Wang Z, Lin Z, Liu M. Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels. Phys Rev E 2002;65: Article no. 051925.
43. Ladd AJC. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J Fluid Mech. 1994;271:311-39.
44. Ladd AJC. Short-term motion of colloidal particles: Numerical simulations via a fluctuating lattice-Boltzmann equation. Phys Rev Lett 1993;70:1339-42.
45. Behrand O. Solid-fluid boundaries in particle suspension simulations via the lattice Boltzmann method. Phys Rev E 1995;52:1164-75.
46. Aidun CK, Lu Y-N. Lattice Boltzmann simulation of solid particles suspended in a fluid. J Stat Phys 1995;81:49-61.
47. Ladd AJC, Verberg R. Lattice Boltzmann simulations of particle-fluid suspensions. J Stat Phys 2001;104:1191-251.
48. Masselo A. A new numerical approach to snow transport and deposition by wind: a parallel lattice gas model. PhD thesis, University of Geneva 2000. http://cui.unige.ch/~chopard/Snow/snow.html.
49. Dupuis A, Chopard B. Lattice gas modeling of scour formation under submarine pipelines. J Comp Phys 2002;178:161-74.
50. Dupuis A. From a lattice Boltzmann model to a parallel and reusable implementation of a virtual river. PhD thesis, University of Geneva, 2002. http://cui.unige.ch/~dupuis/PhD/phd.html.
51. Nie X, Doolen GD, Chen S. Lattice-Boltzmann simulations of fluid flows in MEMS. J Stat Phys 2002;107:279-89.
52. Succi S, Smith G, Kaxiras E. Lattice Boltzmann simulations of reactive microflows over catalytic surfaces. J Stat Phys 2002;107:343-66.
53. Cosgrove JA, Buick JM, Tonge SJ, Greated CA, Campbell DM. Application of the lattice Boltzmann method to oscillatory channel flow; laminar regimes and the primary instability. J Phys A 2003;36:2609-20.
54. Engelund FA. Hydrodynamik. Technical University of Denmark 1968.
55. Mulholland AJ, Steves BA, Buick JM, Cosgrove JA, Collins MW. Simulation of deposit formation in particle laden flows: Thermal properties. Internal Medicine 2003;11:31-8.